a) Define a law of electrostatics in integral form that is used
to compute the electrostatic field E due to a symmetric
distribution of charge within a given volume. State the meaning of
the terms in the defining equation.
b) A uniformly charged long cylinder of radius a and length L
has total charge q inside its volume. What is the direction of the
electric field at points outside the cylinder? Find the electric
field inside and outside the cylinder....
Write a reflection on Maxwell's Equations and how they relate to
each other and physics as well as what they do. Give a break down
to the equations as well as to how they relate to natural
phenonmena
Write the Gauss’s Law for magnetic fields, in details.
mathematical expressions (integral form only) and steps. Explain
each symbol, each detail in each of these equations – by words.
Draw sketches when they are necessary for your explanation.
Show that Maxwell's displacement current must be introduced to
satisfy continuity equation using Gauss' Law, Ampere-Maxwell law
and the fact that divergence of a curl of a vector is 0.
Is there a simple derivation for the probability of measuring
the same spin state for a particle at an angle, theta, to its spin
axis as cos(theta/2) squared if the spin direction is already
known?
Write the Faraday’s Law. mathematical expressions (integral form
only). Explain each symbol, each detail in each of these equations
– by words. Draw sketches when they are necessary for your
explanation.
Snell's Law and the Law of Reflection explain how light is
redirected when it encounters a surface between two media. In the
extreme, light may only reflect at a boundary, and go back into the
medium it was in. More often, some of it reflects and some goes
through. If the boundary is plane and flat, then these laws are
easy to interpret. When the boundary is curved, they describe
happens at every point on the surface. One of the...
Set up an integral for the following scenarios:
Set up the integral in simplified form, do not integrate
a) Arc length of y = ln x , 2 ≤ x ≤ 4 .
b) The surface area generated by rotating y = sin x with respect
to the x-axis, 0 ≤ x ≤ π .
c) The arc length of y = x 2 + 4 , 1≤ x ≤ 3 .
d) The surface area generated by revolving y...